Question

The sum of all odd numbers between 200 and 300 is

Answer 1

201+203+205+207.....+299
50/2 *(201+299)
= 25*500
=12500

Answer 2

Answer:

The sum of all odd numbers between 200 and 300 is 12500.

Step-by-step explanation:

The odd numbers between 200 to 300 are

$201,203,205,...,299$

First term of the AP is 201 and common difference is 2.

Total odd numbers between 200 to 300 are 50.

$S_n=\frac{n}{2}[2a+(n-1)d]$

Where, n is the total number of terms, a is first term and d is common difference.

$S_{50}=\frac{50}{2}[2(201)+(50-1)2]$

$S_{50}=25[402+98]$

$S_{50}=25\times 500$

$S_{50}=12500$

Therefore the sum of all odd numbers between 200 and 300 is 12500.